This is relatively easy, but it requires an astute observation. You use this quite a bit later in topology so I guess it's a good challenge question.

__NOTE__: If you have already seen the solution to this, please don't ruin the fun! This is aimed at people who haven't seen a lot of topology before.

__Problem__: Define

to be the set of all square-summable real sequences

equipped with the metric

. Prove that this metric space is separable.

__Note__: Separable means it contains a countable dense subset. Also, while my book calls this

it is most commonly known as

.